• # question_answer If $A=3\hat{i}+4\hat{j}$ and $B=7\hat{i}+24\hat{j},$the vector having the same magnitude as B and parallel to A is A)            $5\hat{i}+20\hat{j}$ B)                                      $15\hat{i}+10\hat{j}$ C)            $20\hat{i}+15\hat{j}$     D)            $15\hat{i}+20\hat{j}$

$|B|\,=\sqrt{{{7}^{2}}+{{(24)}^{2}}}$ $=\sqrt{625}$ $=25$                    Unit vector in the direction of A will be $\hat{A}=\frac{3\hat{i}+4\hat{j}}{5}$                    So required vector =$25\left( \frac{3\hat{i}+4\hat{j}}{5} \right)\,$ $=15\hat{i}+20\hat{j}$